Skip to main content
  • 203 Accesses

Abstract

In the paper basic concepts of a new methodology of the fuzzy boundary element method are presented. This article deals with fuzzy-set-valued mappings which are solutions of the fuzzy boundary integral equations. Exact fuzzy solutions of fuzzy boundary integral equations are defined as well as conditional solutions. Computational fuzzy problems and applications are considered in details for boundary potential problems with fuzzy Dirichlet and Neumann type boundary conditions and fuzzy density source functions in a fuzzy domain.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Alefeld G., Herzberger J. (1983) Introduction to Interval Computations, Academic Press, New York

    MATH  Google Scholar 

  2. Aumann R. J. (1965) Integrals of Set-Valued Functions, J. Math. Anal. Appl. 12, 1–12

    Article  MathSciNet  MATH  Google Scholar 

  3. Bauch H., Jahn K.U., Oelschlagel, D., Susse, H., Wiebigke, V. (1987) Intervalmathematik, BSG B.G. Teubner Verlagsgeselschaft, Berlin

    Google Scholar 

  4. Brebbia C. A., Dominguez J. (1989) Boundary Elements — An Introductory Course, Comp. Mechanics Publ., Southampton, Boston

    MATH  Google Scholar 

  5. Brebbia C., Telles J. C.F., Wrobel L.C. (1984) Boundary Element Techniques — Theory and Applications in Engineering, Springer-Verlag, Berlin, Heidelberg, New York, Tokyo

    Google Scholar 

  6. Buckley J. J. (1992) Solving Fuzzy Equations in Economics and Finance, Fuzzy Sets and Systems 48, 289–296

    Article  MathSciNet  MATH  Google Scholar 

  7. Buckley J. J. (1992) Solving Fuzzy Equations, Fuzzy Sets and Systems 50, 1–14

    Article  MathSciNet  MATH  Google Scholar 

  8. Buckley J. J., Qu Y. (1990) Solving Linear and Quadratic Fuzzy Equations, Fuzzy Sets and Systems 38, 43–59

    Article  MathSciNet  MATH  Google Scholar 

  9. Buckley J. J., Qu Y. (1990) On Using α-Cuts To Evaluate Fuzzy Equations, Fuzzy Sets and Systems 38, 309–312

    Article  MathSciNet  MATH  Google Scholar 

  10. Buckley J. J., Qu Y. (1991) Solving Fuzzy Equations: A New Solution Concept. Fuzzy Sets and Systems 39, 291–301

    Article  MathSciNet  MATH  Google Scholar 

  11. Buckley J. J., Qu Y. (1991) Solving Systems of Linear Fuzzy Equations. Fuzzy Sets and Systems 43, 33–43

    Article  MathSciNet  MATH  Google Scholar 

  12. BurczyƄski T. (1995) Metoda elementów brzegowych, WN-T, Warszawa

    Google Scholar 

  13. Burczyñski T., Skrzypczyk J. (1995) The Fuzzy Boundary Element Method: A New Solution Concept. Proc. of XII Polish Conference on COMPUTER METHODS IN MECHANICS, Warsaw — Zegrze, Poland, 9–13 May, 65–66

    Google Scholar 

  14. BurczyƄski T., Skrzypczyk J. (1996) Stochastic And Fuzzy Aspects Of The Boundary Element Method, International Conference on Uncertain Structures: Analytical, Numer. and Experimental Methods, Cruise Ship in the Western Caribbean, March 3–10

    Google Scholar 

  15. BurczyƄski T., Skrzypczyk J. (1996) The Fuzzy Boundary Element Method: A New Methodology. Sci. Fasc. of Silesian Tech. Univ., ser. Civil Eng. 83, Gliwice, 25–42

    Google Scholar 

  16. BurczyƄski T., Skrzypczyk J. (1997) Fuzzy Aspects of The Boundary Element Method. Engineering Analysis with Boundary Elements, Special Issue: Stochastic Boundary Element Methods 19, 209–216

    Google Scholar 

  17. BurczyƄski T., Skrzypczyk J. (1997) The Boundary Element Method For Fuzzy Systems. Proc. of the IASTED International Conference on Modelling, Simulation and Optimization, Singapore, August 11–14, 24–27

    Google Scholar 

  18. Dubois D., Prade H. (1979) Fuzzy Real Algebra: Some Results. Fuzzy Sets and Systems 2, 327–348

    Article  MathSciNet  MATH  Google Scholar 

  19. Dubois D., Prade H. (1988) An Approach to Computational Processing of Uncertainty, Plenum Press, New York, London

    Google Scholar 

  20. Felbin C. (1992) Finite Dimensional Fuzzy Normed Linear Space, Fuzzy Sets and Systems 48, 239–248

    Article  MathSciNet  MATH  Google Scholar 

  21. Guang-Quan Z. (1991) Fuzzy Continuous Function and Its Properties, Fuzzy Sets and Systems 43, 159–171

    Article  MathSciNet  Google Scholar 

  22. Kaleva O. (1987) Fuzzy Differential Equations, Fuzzy Sets and Systems 24, 301–317

    Article  MathSciNet  MATH  Google Scholar 

  23. Kaleva O. (1990) The Cauchy Problem For Fuzzy Differential Equations, Fuzzy Sets and Systems 35, 389–396

    Article  MathSciNet  MATH  Google Scholar 

  24. Mikhlin S.G. (1986) Singular Integral Operators, Akademie-Verlag, Berlin

    Book  Google Scholar 

  25. Moore R.E. (1966) Interval Analysis, Prentice Hall, Englewood Cliffs

    MATH  Google Scholar 

  26. Nanda S. (1989) On Integration of Fuzzy Mappings, Fuzzy Sets and Systems 32, 95–101

    Article  MathSciNet  MATH  Google Scholar 

  27. Negoita C.V., Ralescu D.A. (1975) Applications of Fuzzy Sets to System Analysis, Ed. Technica, Birkhauser Verlag, Basel und Stuttgart

    Google Scholar 

  28. Neumaier A. (1990) Interval Methods for Systems of Equations, Cambridge University Press, Cambridge, New York, Port Chester, Melbourne, Sydney

    MATH  Google Scholar 

  29. Nguyen H. T. (1978) A Note on the Extension Principle for Fuzzy Sets, J. of Math. Anal. Appl. 64, 369–380

    Article  MATH  Google Scholar 

  30. Shary S. P. (1996) Algebraic Approach to the Interval Linear Static Identification, Tolerance, and Control problems, or One more Application of Kaucher Arithmetic, Reliable Comp. 2, 3–33

    Article  MathSciNet  MATH  Google Scholar 

  31. Skrzypczyk J. (1996) On Fuzzy Singular Integration. Sci. Fasc. of Silesian Tech. Univ. ser. Civil Eng. 83, Gliwice, 121–130

    Google Scholar 

  32. Skrzypczyk J. (1997) Zadanie brzegowe teorii potencja3u w obszarze rozmytym. MateriaƂy Konferencji naukowej z okazji 70-lecia urodzin Józefa GƂomba pt. Wybrane problemy naukowo — badawcze mostownictwa i budownictwa, Gliwice 17 czerwca 1997, Wyd. Politechniki ƚląskiej, Gliwice, 243–251

    Google Scholar 

  33. Skrzypczyk J., BurczyƄski T. (1997) The Fuzzy Boundary Element Method. Proc. of XIII Polish Conference on COMPUTER METHODS IN MECHANICS, Vol. 4, PoznaƄ, Poland, 5–8 May, 1195–1202

    Google Scholar 

  34. Skrzypczyk J., BurczyƄski T. (1997) Fuzzy Aspects of The Boundary Element Method in Elastostatics. Proc. of XXXVI Sympozjon “Modelowanie w Mechanice”, Wisla 16–20 luty 1997, Zeszyty Naukowe Katedry Mechaniki Stosowanej 3, 25–30

    Google Scholar 

  35. Skrzypczyk J., BurczyƄski T. (1998) Metoda elementów brzegowych dla obszarów o ksztaƂcie rozmytym, MateriaƂy XXVII Sympozjonu “Modelowanie w Mechanice”, WisƂa 9–13 lutego 1998, Zeszyty Naukowe Katedry Mechaniki Stosowanej 6, 317–322.

    Google Scholar 

  36. Skrzypczyk J., BurczyƄski T. (1998) Fuzzy Boundary Element Method in the Analysis of Uncertain Systems, J. of Theoretical and Applied Mechanics 36, 493–512

    MATH  Google Scholar 

  37. Skrzypczyk J., BurczyƄski T. (1998) Boundary Element Methods For Fuzzy Domain, Proc. of IABEM International Symposium on Boundary Element Methods, Ecole Polytechnique, Palaiseau (Paris), France, May 26–29

    Google Scholar 

  38. Skrzypczyk J., Witek H. (2000) Solution Interpretation in Fuzzy Boundary Problems — New Concepts, Proc. of XXXVI Sympozjon “Modelowanie w Mechanice”, WisƂa 14–18 luty 2000, Zeszyty Naukowe Katedry Mechaniki Stosowanej, 285–288

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2001 Springer Science+Business Media Dordrecht

About this paper

Cite this paper

Skrzypczyk, J., BurczyƄski, T. (2001). Theoretical and Computational Aspects of the Fuzzy Boundary Element Methods. In: Burczynski, T. (eds) IUTAM/IACM/IABEM Symposium on Advanced Mathematical and Computational Mechanics Aspects of the Boundary Element Method. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-9793-7_30

Download citation

  • DOI: https://doi.org/10.1007/978-94-015-9793-7_30

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-90-481-5737-2

  • Online ISBN: 978-94-015-9793-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics